With all of the excitement and hands on learning from the last couple of days, I like to give my students the opportunity to start class by asking follow up questions. To help promote high quality questions, I ask them to meet in groups of 3-4 and review their notes from the activity with the accident reconstructionist. (I have found that if I don't do this, then I hear nothing but crickets.) As they work, I try to visit each group and be involved briefly in their conversation. This whole process will probably take no more than 5 minutes. After allowing the students to discuss, I bring the group back together and open it up to questions.
When I have done this activity in the past, the students ask a lot of questions about the career of an accident reconstructionist and many other questions that I am unable to answer as a math teacher. This allows me to model an important life skill to my students - when I don't know the answer to the question, I pass it along to someone who does! In my follow up thank-you email to our guest police officer, I attach these follow up questions and read the answers to the class when he responds the next day.
It may be beneficial to have the PowerPoint Accident Reconstruction PPT #2 - Math Modeling Discussion.pptx on hand in case the students would like to reference it with their follow up questions.
Prior to diving deeper into the mathematics, I like to take time with my students to define the difference between Radical Equations and Equations Containing Radicals. As we seek to build our students mathematical arsenal on the math practice standards, it is important to take time to question the differences in structure between various types of operations and equations. Radical Equations and Linear Equations help to provide this first platform for students, because in the past, most of what they have studied has been linear.
In the PowerPoint, the students are asked to identify differences between two equations that are given. When I display the slideshow and begin the investigation, I ask the students to quietly write down in their notes any observations that they see. Having the students do this quietly allows everyone the chance to process what is on the screen. I have made the mistake before of opening up immediately to student comments, and I can tell you that it is much better to let everyone answer the question instead of only to fastest 1-2 students.
After allowing the students to think for 2-3 minutes (and stepping to the back of the classroom and locking my lips so that I don't give away any hints - its part of being a math teacher and wanting to help kids) I ask my students to begin sharing out their observations and we make a list on the board. I strategically call on a few students who normally take a little longer to process for the "obvious" observations, and then ask for any additional observations from the class. It is really cool when a student says:
"Well, I saw the word "linear" and I remember that from Algebra I. I tried to graph them both by plotting points and this is what it looked like."
Yes, this is living in a perfect world.... but hey, it could happen! In all seriousness, to promote this type of thinking (MP2 and MP7) I drop a scrap coordinate grid on several of the students desks as I see they are finishing up their initial observations in their notes. After receiving this special delivery, most of them take the hint!